SOLUTION: Hello, I have an algbra word problem that's driving me nuts. Here it is: Staples sells cartons of pens ($9) and rubber bands($4). Leona ordered a total of 36 cartons for $284. Ho

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hello, I have an algbra word problem that's driving me nuts. Here it is: Staples sells cartons of pens ($9) and rubber bands($4). Leona ordered a total of 36 cartons for $284. Ho      Log On

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Question 267070: Hello, I have an algbra word problem that's driving me nuts. Here it is:
Staples sells cartons of pens ($9) and rubber bands($4). Leona ordered a total of 36 cartons for $284. How many cartons of each did Leona order?
Found 2 solutions by scott8148, ptaylor:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
p + r = 36 ___ r = 36 - p

9p + 4r = 284

substituting the "equivalent value" for r ___ 9p + 4(36 - p) = 284

9p + 144 - 4p = 284 ___ 5p = 140 ___ p = 28

substituting the "equivalent value" for p ___ r = 36 - (28) = 8

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of cartons of pens ordered
The pens cost 9x dollars
Then 36-x=number of cartons of rubber bands ordered
The rubber bands cost 4(36-x) dollars
Now we are told that the above (pens and rubber bands) cost a total of 284 dollars, so:
9x+4(36-x)=284 get rid of parens
9x+144-4x=284 subtract 144 from erach side
9x+144-144-4x=284-144 collect like terms
5x=140
x=28 --------------number of cartons of pens
36-x=36-28=8 number of cartons of rubber bands
CK
28*9+8*4=284
252+32=284
284=284
If you like, you can also solve this problem using two equations and two unknowns:
Let x=number of cartons of pens
And let y=number of cartons of rubber bands
x+y=36-----------------eq1
9x+4y=284----------------eq2
multiply eq1 by 4 and subtract it from eq2 and we get:
5x=140
x=28-------------same as before
you can finish
Hope this helps----ptaylor